There is a simple reason for why time travel into the past isn’t possible. Everything revolves in a predictable motion from sub atomic particles all the way up to planets around their suns and galaxies. With these rotations charges are exchanged or kept at atomic and subatomic levels, and everything works in reaction causing what we see as life or existence. There is no historical record of space-time (space time is simply man’s observation), and changes and fluctuations based on subatomic inconsistencies and interactions exist; random chaos at atomic levels.
Without a record of spacetime going backward in time would mean that some reactions might reverse while others which are unpredictable would not (eg. nuclear chain reactions). If you could move at the speed of light around the sun (matter can't travel that fast) you would simply be traveling around the sun at the speed of light in whichever direction desired... sorry Star Trek fans... no whales today.
The closest thing, involving stasis… a physical recording.
If you record all of the particles in motion as an event happens in some system you might be able to recreate a representation of the scene of the event using the involved structures, but you can not recreate the event itself, you can only alter the replayed recreation or arrangement of molecules and atoms. All matter would have to be contained in a confined space, and all molecular motion would need to be stopped in that confined space, in order to accurately recreate an event and capture all involved components at a sub-atomic level; thermodynamic equilibrium would need to be achieved to insure a proper record. To record all of the particles without interfering with their structure would require disassembly for a proper mapping; a deconstruction.
The process of structural recording should never, ethically be done on a living sentient thing which would also prevent things such as teleportation or exact atomic cloning of living organisms. The reason for this is because stopping all atoms in their present state would cause their [natural] interactions to fail and their atomic structures would be disrupted. If the matter was not stopped prior to recording, the speed of the atomic breakdown could prove extremely painful and the instantaneous reactions between cells in the organism would make the recorded position of the future recorded cells in a state of reaction. Imagine burning every cell off of your body one cell at a time, the reassembled image of the original (yourself) would contain evidence of the trauma because you couldn’t record all of the cells in their paused molecular subatomic state at the same time. This is all of course based on the organism itself surviving the pause or deceleration to maximum entropy.
Furthermore upon reassembly if the recorded cells were to be rearranged there would be a chance of accidentally creating an excited nucleus causing a fission reaction.
I would like to state that I've not studied these things at any level at all and this is simply my uneducated hypothesis based on my observation.
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I'm going to read this before it goes live if you don't mind.